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Field enhancement is an interesting and important topic in electromagnetic study. Electromagnetic field concentration and enhancement devices have wide applications in high directional antenna design, laser ignition, optical control, etc. At present, there are usually two ways of implementing the field enhancement, one is to use the artificial electromagnetic materials to realize the radiation direction control and energy concentration, which is more suitable for the applications at microwave or lower frequencies, and the other is to use the materials with high permittivity or high permeability. However, the latter is extremely sensitive to the position and characteristic of the radiation source and the cross-sectional area of the material, and depends heavily on the value of the relative permittivity or the relative permeability of the material. Therefore, both methods cannot fully meet the application requirements of creating high field intensity in optical band, such as laser ignition, etc. In this paper, based on the theory of photonic crystal doping, the strong electromagnetic field enhancement has been successfully realized by epsilon-near-zero medium filled with ordinary dielectric dopant. We first make the comprehensive theoretical analysis of the field enhancement in the structure of epsilon-near-zero medium with dielectric dopant. The method of calculating the central magnetic field in the doped medium is then rigorously derived, and the formula for the ratio of the central magnetic field in the doped medium to the external radiation field is deduced. We find that the optimal magnetic field enhancement occurs only when the proposed structure is equivalent to an epsilon-mu-near-zero medium. Subsequently, under the above condition, various parameters (radius of the cylindrical dopant, number of sources, etc.) are studied to analyze the magnetic field enhancement performance inside the doped medium. The theoretical analysis and simulation results show that the proposed structure can significantly enhance the magnetic field which is applicable in a broad frequency band from microwave to optical region, and meets the application requirements of providing high field intensity. Finally, as a practical realization example, an ultraviolet ignition device working at 270 nm is designed, which presents an efficient and alternative way of developing electromagnetic (optical) devices for producing strong field enhancement.
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Keywords:
- epsilon-near-zero medium /
- dielectric dopant /
- field enhancement
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图 1 ENZ介质掺杂介质结构等效示意图(2D截面) (a) ENZ媒质掺杂介质结构截面图, 存在一个与截面垂直的磁流IM; (b) 具备相同截面大小的等效ENZ介质示意图, 在该截面相同的位置存在一个与图(a)相同的的磁流IM
Figure 1. Schematics of magnetic ENZ medium filled with dielectric dopants: (a) A 2D magnetic ENZ medium with several macroscopic non-magnetic dielectric dopants and an alternating magnetic current IM embedded in the ENZ medium whose magnetic field H1 is polarized along y axis; (b) the equivalent homogeneous 2D ENZ medium with the same cross-sectional shape and near-zero permittivity, but a uniform equivalent relative permeability μeff
图 2 ENZ媒质介质掺杂后其等效磁导率μeff随掺杂介质半径的变化
Figure 2. Effective relative permeability (μeff) of the doped ENZ medium as a function of the doping rod radius.
图 3 掺杂介质具有不同半径时, 其内部中心磁场相对外辐射场的磁场增强倍数计算与仿真验证 (a) 掺杂介质内部中心磁场与其半径的关系曲线; (b) 理想点源的磁场仿真结果; (c), (d), (e) 掺杂介质半径分别为rd/λ0 = 0.158, rd/λ0 = 0.363和rd/λ0 = 0.572时掺杂介质ENZ媒质结构的磁场仿真结果
Figure 3. Enhancement factors of internal magnetic field in the dopant compared with external radiation field with the different radius of dopant: (a) Enhancement factors of internal magnetic field in the dopant with different rd; (b) the simulation result of magnetic field of point source in free space; (c), (d), (e) simulation results of magnetic field in ENZ filled with dopant with different radius of dopant (rd/λ0 = 0.15659, 0.35958, 0.56427), respectively.
图 4 掺杂介质的ENZ媒质结构分别包含单个点源和两个点源时的磁场对比仿真 (a) 掺杂介质的ENZ媒质结构包含单个点源的磁场仿真结果(εr1 = 6, rd/λ0 = 0.158); (b) 在图4(a)结构中再增加一个点源的磁场仿真结果; (c) 调整4(b)结构两个点源位置的磁场仿真结果; (d) 改变图4(c) ENZ媒质截面形状后的磁场仿真结果(点源位置任意调整, ENZ截面积不变)
Figure 4. Simulation results of magnetic field in ENZ medium filled with the dopant containing different point sources, respectively: (a) One point source embedded in the ENZ medium (εr1 = 6, rd/λ0 = 0.158); (b) two point sources embedded in the ENZ medium; (c) two point sources located somewhere in ENZ medium; (d) two point sources embedded in an ENZ square (with the same cross section).
图 5 265—275 nm紫外光波段点火器件的计算分析与仿真验证 (a) 265—275 nm波段银的相对介电常数以及掺杂介质的银薄膜的等效磁导率计算曲线; (b) 270 nm波长掺杂介质的银薄膜的磁场分布仿真结果
Figure 5. Analysis and simulation of ignition device at wavelength of 270 nm: (a) The relative permittivity of silver film (red line) and the effective relative permeability of silver film filled with dielectric dopant at wavelength of 263 nm to 275 nm (blue line); (b) the simulation result of magnetic field in silver film filled with dielectric dopant at wavelength of 270 nm (rd/λ0 = 0.2261, εrd = 3).
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[1] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
Google Scholar
[2] Fante R L, McCormack M T 1988 IEEE Trans. Antennas Propag. 36 1443
Google Scholar
[3] Yang J, Shen Z 2007 IEEE Antennas Wirel. Propag. Lett. 6 388
Google Scholar
[4] Fu W, Liu S, Fan W 2007 J. Magn. Magn. Mater. 316 54
Google Scholar
[5] Munk B A 2009 Metamaterials: Critique and Alternatives (New Jersey: John Wiley & Sons) pp160–168
[6] Costa F, Monorchio A 2012 IEEE Trans. Antennas Propag. 60 2740
Google Scholar
[7] Li B, Shen Z 2013 IEEE Trans. Microwave Theory Tech. 61 3578
Google Scholar
[8] Liu T, Cao X, Gao J 2013 IEEE Tran. Antennas Propag. 61 1479
Google Scholar
[9] Li B, Shen Z 2014 IEEE Tran. Antennas Propag. 62 130
Google Scholar
[10] Liu Y, Zhao X 2014 IEEE Antennas Wirel. Propag. Lett. 13 1473
Google Scholar
[11] Youngworth K S, Brown T G 2000 Opt. Express 7 77
Google Scholar
[12] Novotny L, Zurita-Sánchez J R 2002 J. Opt. Soc. Am. B 19 2722
Google Scholar
[13] Zhan Q 2009 Adv. Opt. Photonics 1 1
Google Scholar
[14] Veysi M, Guclu C, Capolino F 2015 J. Opt. Soc. Am. B 32 345
Google Scholar
[15] Pendry J B, Holden A J, Robbins D J, Stewart W J 1999 IEEE Trans. Microwave Theory Tech. 47 2075
Google Scholar
[16] Marqués R, Medina F, Rafii-El-Idrissi R 2002 Phys. Rev. B 65 144440
Google Scholar
[17] García-Etxarri A, Gómez-Medina R, Froufe-Pérez L S, López C, Chantada L, Scheffold F, Aizpurua J, Nieto-Vesperinas M, Sáenz J J 2011 Opt. Express 19 4815
Google Scholar
[18] Liberal I, Li Y, Engheta N 2017 Philos. Trans. A 375 20160059
Google Scholar
[19] Jin Y, He S 2010 Opt. Express 18 16587
Google Scholar
[20] Jin Y, Zhang P, He S L 2010 Phys. Rev. B 81 085117
Google Scholar
[21] Zhong S, He S 2013 Sci. Rep. 3 2083
Google Scholar
[22] Silveirinha M G, Belov P A 2008 Phys. Rev. B 77 233104
Google Scholar
[23] Liu R, Roberts C M, Zhong Y, Podolskiy V A, Wasserman D 2016 ACS Photonics 3 1045
Google Scholar
[24] Zhou Z H, Li Y, Li H, Sun W Y, Liberal I, Engheta N 2019 Nat. Commun. 10 4132
Google Scholar
[25] Pacheco-Peña V, Engheta N, Kuznetsov S, Gentselev A, Beruete M 2017 Phys. Rev. Appl. 8 034036
Google Scholar
[26] Silveirinha M, Engheta N 2007 Phys. Rev. B 75 075119
Google Scholar
[27] Xu J, Song G, Zhang Z, Yang Y, Chen H, Zubairy M S, Zhu S 2016 Phys. Rev. B 94 220103
Google Scholar
[28] Liu R, Cheng Q, Hand T, Mock J J, Cui T J, Cummer S A, Smith D R 2008 Phys. Rev. Lett. 100 023903
Google Scholar
[29] Guo Z Y, Wu F, Xue C H, Jiang H T 2018 J. Appl. Phys. 124 103104
Google Scholar
[30] Zhang Z F, Xue C H, Jiang H T, Lu H 2013 Appl. Phys. Lett. 103 201902
Google Scholar
[31] Liberal I, Mahmoud A, Li Y, Edwards B, Engheta N 2017 Science 355 1058
Google Scholar
[32] Wang Z R, Hu T, Tang L W, Ma N, Song C L, Han G R, Weng W J, Du P Y 2008 Appl. Phys. Lett. 93 222901
Google Scholar
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